@PhillipHamlyn Thank you for joining in, interesting comments.
I must say, though, the Gartner definition of SaaS you cite is so impossibly broad as to be totally useless. If all it takes is a subscription contract and remote management, then my family's Microsoft Office, for which I pay an annual subscription and which is kept up-to-date by Office Update, counts as a SaaS application - which patently it is not. The SaaS version is Office 365 although it is only partially SaaS since the client (unless you use the web version) still runs on the desktop.
I believe the NIST definition often gets misinterpreted because it describes three separate cumulative layers: IaaS, PaaS and SaaS. While it's possible to host a client-server application on IaaS and deliver it from the cloud, that doesn't make it SaaS. To be described as a cloud application per the NIST definition, an application has to include core architectural features in the definition such as resource pooling and elasticity. Otherwise it's just SoSaaS sitting on IaaS, and hugely inefficient/unwieldy.
I'm interested to see integration and big data cited as advantages of cloud SaaS - I think those are good points. I know I'm a bit of an interloper here but in the interests of stimulating discussion, here's a list of cloud-native SaaS benefits that I included in a recent article on client-server vs cloud SaaS: